(Q7)The diameter of a metallic sphere is 6 cm. It is melted and drawn into a long wire having a circular cross section of diameter as 0.2 cm. Find the length of the wire.

6 cm 0.2 cm

Diameter of metallic sphere = 6cm.

∴ Radius of metallic sphere = r1= 3cm.

Now, diameter of cross-section of cylindrical wire = 0.2 cm

∴ Radius of cross section of cylinder wire = r2 = 0.1 cm.

Let the length of wire be l cm.

Since the metallic sphere is converted into a cylindrical shaped wire of length h cm.

Volume of the metal used in wire = Volume of the sphere

π × r22 × h =
4
3
 × π × r13
π × ( )2 × h =
4
3
 × π × ( )3
π × (
1
 )2 × h =
4
3
 × π ×
π ×
1
 × h = π
h =
π ×
π
 cm = cm = m

Therefore, the length of the wire is m.